This detailed map of the landscape of mathematics was designed by Martin Kuppe as part of his recent YouTube video Mathematics: Measuring times laziness squared. As well as being humorous, the picture also illustrates the relationships between the major areas of mathematics, such as algebra, geometry, topology, and analysis. The picture is very detailed and is worth viewing at high resolution.

The video, which you can see at http://goo.gl/3Rg8jd, is well worth twenty minutes of your time. It gives an overview of mathematics in a way that should be comprehensible to an intelligent general audience. The sense of humour in the videos reminded me of the writing of Douglas Adams. Something I found especially remarkable is that the video manages to explain the gist of what algebraic topology is in a few minutes, without getting technical. (Algebraic topology aims to understand topological structures by associating algebraic objects to them.)

The map contains various visual and verbal jokes about mathematics; some of these are explained in the video, but others are not. I liked the names of the plains: have a look for the Complex Plain, the Projective Plain and the xy-Plain. The buildings in Statistigrad look like normal distributions and histograms. The fields in the picture are actual fields, but this is a reference to the algebraic notion of a field, which roughly speaking is a structure in which one can do addition, subtraction, multiplication and division. (This is not directly related to the use of the term field in physics.)

As an algebraist, I particularly enjoyed the Califate of Al-Gebra, with the Al separated as if it were an Arabic article. This is appropriate because the English word algebra comes from the Arabic term al-jebr, meaning “reunion of broken parts”. In case you're wondering, califate is an acceptable variant spelling of caliphate.

I was very surprised that Martin Kuppe/Zogg doesn't have a much bigger following on social media, given the high quality of his output. You can follow him as ZoggFromBetelgeuse on YouTube, or as ZoggTheAlien on Twitter. One of his recent tweets contains links to various versions of Mathematistan, including this picture.